Question

A crime is observed by a group of n people. Each person would like the police to be informed, but prefers that someone else make the phone call. Specifically, suppose that each person attaches the value v to the police being informed and bears the cost cif she makes the phone call, where v >c>0. Then the situation is modeled by the following strategic game. Players: The n people. Actions: Each player's set of actions is {Call, Don't call}. Payoffs: A player will get 0 if no one calls, a player gets v -c whenever she makes the call, a player will get v if someone else makes the call. a) Find all of the Nash equilibria of this game.

Answer 1

1. the game has n pure Nash equilibria in which exactly one person halls. " When the person switches forcom calling to not calling the payoff falls from TV - c>0 to O. » G somebody else switches to alling & the pays rayoff falls orto vrc 2. the game has no other pure Nash Isliramu Is It no one calls, any person can switch to calling and raise her payoff from o to v-e. If two or more persons calle, then any of them can switch to not calling and raise her payoff from v-ato v cscanned with CamScanner

op Nash on such a ummetric mixed equibbrum probalulity that each person calls cocp<1 and bet P = (P); EN For each person i, Up (call, P-i ) = Up (Don't call, P-8) Nowe, Uil Call, P- ;) = V-C and, Uil Don't call, P-1) = 0. Prena one lese calls} tv.fre at least one calls tv. (1-P) { no one calls? and the eginhlirium conditionis un-c = v.21-Pr{ no one lise calls S = Po & no one the calls) 34 = (1-P)n-1 >>p=17 (5) no € (0,1)